Conventions, Definitions, Identities, And Other Useful Formulae,
2024
Loyola University Chicago
Conventions, Definitions, Identities, And Other Useful Formulae, Robert A. Mcnees Iv
Physics: Faculty Publications and Other Works
As the name suggests, these notes contain a summary of important conventions, definitions, identities, and various formulas that I often refer to. They may prove useful for researchers working in General Relativity, Supergravity, String Theory, Cosmology, and related areas.
The Law Of The Iterated Logarithm For Lp-Norms Of Kernel Estimators Of Cumulative Distribution Functions,
2024
Illinois State University
The Law Of The Iterated Logarithm For Lp-Norms Of Kernel Estimators Of Cumulative Distribution Functions, Fuxia Cheng
Faculty Publications – Mathematics
In this paper, we consider the strong convergence of Lp-norms (p ≥ 1) of a kernel estimator of a cumulative distribution function (CDF). Under some mild conditions, the law of the iterated logarithm (LIL) for the Lp-norms of empirical processes is extended to the kernel estimator of the CDF.
Counting Conjugates Of Colored Compositions,
2024
Georgia Southern University
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Honors College Theses
The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.
Analysis Of Sir Model With Optimal Control Strategy For A Simple Traffic Congestion Process,
2024
Universitas Diponegoro
Analysis Of Sir Model With Optimal Control Strategy For A Simple Traffic Congestion Process, Ratna Herdiana, Zani Anjani Rafsanjani, R. Heru Tjahjana, Yogi Ahmad Erlangga, Moch Fandi Ansori
All Works
Traffic analysis on highways at the macroscopic level is very similar to the analysis of the spread of infectious diseases, namely the susceptible-infected-recover (SIR) model. We propose the SIR model with a control variable. The dynamics with fixed control and stability of the model are analyzed. Sensitivity analysis was also carried out. Variable control is applied as an effort to regulate or change the duration of the green light at an intersection. We obtain an optimal control strategy when the control is time-dependent. Numerical results show the positive impacts of implementing the control to susceptible vehicles and treatment for congested …
Order-2 Delaunay Triangulations Optimize Angles,
2024
The University of Texas Rio Grande Valley
Order-2 Delaunay Triangulations Optimize Angles, Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The local angle property of the (order-1) Delaunay triangulations of a generic set in R2 asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation is the only one that has the local angle property. …
P-Adic Quantum Mechanics, The Dirac Equation, And The Violation Of Einstein Causality,
2024
The University of Texas Rio Grande Valley
P-Adic Quantum Mechanics, The Dirac Equation, And The Violation Of Einstein Causality, Wilson A. Zuniga-Galindo
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We introduce a new p-adic Dirac equation that predicts the existence of particles and antiparticles and charge conjugation like the standard one. The new equation shares many properties with the old one. However, the space's discrete (p-adic) nature imposes substantial restrictions on the solutions of the new equation. This equation admits localized solutions, which is impossible in the standard case. Finally, we show that a quantum system whose evolution is controlled by the p-adic Dirac equation does not satisfy the Einstein causality.
Modeling The Effect Of Observational Social Learning On Parental Decision-Making For Childhood Vaccination And Diseases Spread Over Household Networks,
2024
The University of Texas Rio Grande Valley
Modeling The Effect Of Observational Social Learning On Parental Decision-Making For Childhood Vaccination And Diseases Spread Over Household Networks, Tamer Oraby, Andras Balogh
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős–Rényi (random) networks or Barabási–Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, …
Infusing Machine Learning And Computational Linguistics Into Clinical Notes,
2024
Sova Southeastern University
Infusing Machine Learning And Computational Linguistics Into Clinical Notes, Funke V. Alabi, Onyeka Omose, Omotomilola Jegede
Mathematics & Statistics Faculty Publications
Entering free-form text notes into Electronic Health Records (EHR) systems takes a lot of time from clinicians. A large portion of this paper work is viewed as a burden, which cuts into the amount of time doctors spend with patients and increases the risk of burnout. We will see how machine learning and computational linguistics can be infused in the processing of taking clinical notes. We are presenting a new language modeling task that predicts the content of notes conditioned on historical data from a patient's medical record, such as patient demographics, lab results, medications, and previous notes, with the …
Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions,
2024
The University of Texas Rio Grande Valley
Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified.
Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons,
2024
The University of Texas Rio Grande Valley
Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this paper, we have investigated the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where m≥3, inscribed in a unit circle.
A Spiral Workbook For Discrete Mathematics 2nd Edition,
2024
SUNY Fredonia
A Spiral Workbook For Discrete Mathematics 2nd Edition, Harris Kwong
Milne Open Textbooks
This updated text covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is …
Open Diameter Maps On Suspensions,
2024
Missouri University of Science and Technology
Open Diameter Maps On Suspensions, Hussam Abobaker, Włodzimierz J. Charatonik, Robert Paul Roe
Mathematics and Statistics Faculty Research & Creative Works
It is shown that if X is a metric continuum, which admits an open diameter map, then the suspension of X, admits an open diameter map. As a corollary, we have that all spheres admit open diameter maps.
Festival Of Research Abstracts, 2024,
2024
Wright State University
Festival Of Research Abstracts, 2024, College Of Science And Mathematics, Wright State University
Festival of Research
The collection of abstracts accepted for the 2024 Festival of Research hosted by the Wright State University College of Science and Mathematics.
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders,
2024
Wilfrid Laurier University
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen
Theses and Dissertations (Comprehensive)
The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …
Pre-Calculus: Thinking Deeply About Simple Things,
2024
Georgia College
Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter
Graduate Research Showcase
“Pre-Calculus: Thinking Deeply About Simple Things” is a research-based creative endeavor focused on designing a high-school pre-calculus course. This course aims to foster deep, meaningful thinking, as well as an appreciation of the values of diversity, equity, and inclusion in the math classroom. The course leverages students’ funds of knowledge to employ culturally responsive teaching methods to connect mathematical concepts to the students’ backgrounds, interests, and real-life situations. This course also integrates social-emotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problem-based learning, the course …
The Deep Bsde Method,
2024
Missouri University of Science and Technology
The Deep Bsde Method, Daniel Kovach
Masters Theses
"The curse of dimensionality is the non-linear growth in computing time as the dimension of a problem increases. Using the Deep Backwards Stochastic Differential Equation (Deep BSDE) method developed in [HJE18], I approximate the solution at an initial time to a one-dimensional diffusion equation. Although we only approximate a one-dimensional equation, this method extends well to higher dimensions because it overcomes the curse of dimensionality by evaluating the given partial differential equation along "random characteristics''. In addition to the implementation, I also present most of the mathematical theory needed to understand this method"-- Abstract, p. iii
Recommendations To Internal Auditors Regarding The Auditing And Attestation Of Mathematical Programming Models,
2024
Loyola Marymount University
Recommendations To Internal Auditors Regarding The Auditing And Attestation Of Mathematical Programming Models, Jose Rincón, Greg Akai, Daryl Ono
LMU Librarian Publications & Presentations
Mathematical programming planning models increase operational efficiency and minimize operating costs, but the underlying mathematics generally is complex. Combinatorial optimization is technically sophisticated which requires a strong quantitative background to successfully implement. Most internal auditors will not have the technical training to critically assess the underlying mathematics of mathematical programming planning models, but the internal auditor can still provide insight and attestation which can increase the efficiency of mathematical programming planning models.
A Little More On Ideals Associated With Sublocales,
2024
Chapman University
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
Mathematics, Physics, and Computer Science Faculty Articles and Research
As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the Stone- Čech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper …
Solutions To The Kaluza-Klein Field Equations,
2024
Minnesota State University, Mankato
Solutions To The Kaluza-Klein Field Equations, Abel Eshete
All Graduate Theses, Dissertations, and Other Capstone Projects
This Alternate Paper Plan explores Kaluza-Klein theory, a multidimensional framework designed to unify Einstein’s gravitational field theory and Maxwell’s electromagnetic field theory. The objectives of this research can be summarized in two key areas: The first objective is to present a comprehensive introduction to the compactified Kaluza-Klein theory. The second aim involves the application of differential geometry, specifically E ́lie Cartan’s tetrad formalism, to derive exact solutions in two distinct scenarios: a. A Levi-Civita spacetime, b. A general spherical system. Furthermore, Lagrangian and Hamiltonian formalism are utilized to define stability conditions and describe gravitational lensing and Precession of Perihelion within …
Conditional Constrained And Unconstrained Quantization For Probability Distributions,
2024
The University of Texas Rio Grande Valley
Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we present the idea of conditional quantization for a Borel probability measure P on a normed space Rk. We introduce the concept of conditional quantization in both constrained and unconstrained scenarios, along with defining the conditional quantization errors, dimensions, and coefficients in each case. We then calculate these values for specific probability distributions. Additionally, we demonstrate that for a Borel probability measure, the lower and upper quantization dimensions and coefficients do not depend on the conditional set of the conditional quantization in both constrained and unconstrained quantization.
